If the home is on a private well and the air test came back elevated, yes. Waterborne radon is released into the air during showers and laundry. Homes on municipal water do not need this test, because treatment removes it.
More detail
Radon reaches a house two ways. The dominant path everywhere is soil gas entering through the foundation, which is what a mitigation system addresses. The second path only matters for private wells: groundwater picks up radon from the same bedrock, and the gas comes out of solution when the water is agitated, which means showers, dishwashers, and washing machines release it into the air of the house. Municipal supplies do not carry this problem in practice. Water sits in open reservoirs and travels through treatment and distribution long enough that dissolved radon has escaped before it reaches a tap. If the home is on city water, skip this test. For private wells the rough working figure used in the field is that roughly 10,000 pCi/L of radon in water contributes about 1 pCi/L to indoor air. That ratio is why water testing is usually a second step rather than a first: air testing tells you whether there is a problem at all, and water testing tells you how much of it the well is contributing. Treatment is a separate system from air mitigation. The two established methods are aeration, which strips the gas from the water before it enters the house and is generally the more effective option, and granular activated carbon, which is cheaper up front and requires managing the accumulated radioactivity in the media over time. A note on water softeners, which come up constantly: a softener exchanges hardness minerals and does nothing for radon. Neither does a standard sediment or taste-and-odor filter. Private wells cluster in the outer parts of Franklin, Delaware, Licking, and Fairfield counties rather than the built-up areas, so this test is relevant to a minority of homes across Greater Columbus and Central Ohio. On a public supply, skip it.